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Seminar

DDC - Online Seminar: Measures on perfect PAC fields December 04, 2020 (09:00 AM PST - 10:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Zoé Chatzidakis (Centre National de la Recherche Scientifique (CNRS))
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

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Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract: This is work in progress, joint with Nick Ramsey (UCLA).

 

A conjecture, now disproved by Chernikov, Hrushovski, Kruckman, Krupinski, Pillay and Ramsey, asked whether any group with a simple theory is definably amenable. It is well known that the counting measure on finite fields gives rise to a non-standard counting measure on pseudo-finite fields (the infinite models of the theory of finite fields). It was unknown whether other PAC fields possessed a reasonable measure, and in this talk, we will show that some of them do, although the measure we define does not have all the nice properties of a counting measure when the field is not pseudo-finite.  This result can be used to show that if G is a group definable in an e-free perfect PAC field, then G is definably amenable.



We hope to extend our results to the wider class of bounded perfect PAC fields.

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